Answer: 54 degrees
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Step-by-step explanation:
Angle A' is given to be 59 degrees. Due to the symmetry of the reflection, this is also the measure of angle A as well. Angle B is shown to be 67 degrees.
Angles A,B,C add to 180 degrees. This is true for any three angles of a triangle.
A+B+C = 180
59+67+C = 180
126+C = 180
C+126 = 180
C+126-126 = 180-126 ... subtract 126 from both sides
C = 54
Extra info: The side lengths of 61 and 57 are never used.